Proper design of a load carrying structure requires attention to the cost, weight, and durability of the structure. Effective design requires an understanding of the loads and deflection which the structure undergoes during its lifetime. With highly engineered parts the very feasibility of a machine or structure may require advanced design techniques.
Computer based mathematical structural models of structures, such as those employing Finite Element Analysis (FEM), are widely used to help the designer simulate structures and imposed loads. While often helpful, a mathematical model is only as good as the correlation between the model equations and the real world. To test this correlation, designers must fabricate real parts and subject them to physical loads. The results of experiments on real world test structures are used to improve the mathematical models. Comparison of the physical results to those predicted by the mathematical model aids the designed in developing equations and constants which more closely model the real world.
The classical approach to determining stresses within a structure in the real world is to apply strain gauges to the object and measure the induced strains when the structure is loaded. Strain gauges, while accurate, provide information only about a limited number of points on the structure and do not allow easy visualization of the stresses produced in a structure.
Recently, new techniques that allow rapid capture of full field stresses over the surface of an entire structure or portion of a structure have been developed. These techniques such as Thermoelastic Stress Analysis (TSA) have allowed tension and compression loads to be rapidly determined for every point on a structure. These new techniques allow visualization of the imposed strains and displacement in objects being tested.
The structural analysis technique known as Photoelastic Stress Analysis (PSA) has been recognized as having great potential because it can be used to determine shear stresses within a structure directly.
Thermoelastic Stress Analysis detects minute changes in temperature due to compression or expansion of a structure. Expansion and compression correspond to tensile and compressive forces within a structure. Shear stresses must be derived from a knowledge of the observed tensile and compressive forces. Photoelastic Stress Analysis which can provide direct imaging of shear stresses thus provides the missing ingredient to complete characterization of a loaded structure. In addition Photoelastic Stress Analysis can be performed by statically loading a structure. In many cases statically loading a structure will be significantly less costly than the dynamic loading required for Thermoelastic Stress Analysis. Maximum understanding of a structure is achieved by employing both TSA and PSA.
PSA is based on the observation that some materials respond to stress by increasing the speed of light through the material along the plane of the imposed stress. The orientation of the increased speed of light is referred to as the fast axis. A slow axis is defined perpendicular to the fast axis. Where the principal stresses are unequal in magnitude, or differ in sign, such materials exhibit birefringence. Birefringence is a property of an optically transparent material which causes the velocity of light through the material to vary depending on the vibrational plane of the light. The amount of birefringence present in an object is proportional to the difference between the principal stresses, which defines the shear stresses within the object. To apply Photoelastic Stress Analysis techniques, a test model must be constructed of, or coated with, a birefringent material.
When plane polarized light from a first polarizer passes through a birefringent material in which the fast axis is tilted with respect to the axis of the polarized light, the polarized light is resolved into two perpendicular components, a first component along the fast axis and a second component along the slow axis, thereby producing two components of the linearly polarized light which are separated in time. When the fast axis and slow axis components are viewed through a second polarizing filter, referred to as an analyzer, which is arranged perpendicular to the orientation of the first polarizer, a component of each of the first and second components will be able to pass through the second polarizing filter or analyzer. Because the first and second components which pass through the birefringent material are separated in time they are not fully recombined by the analyzer but each component is resolved into a portion which is parallel to the analyzer and thus can pass through the analyzer.
This type of optical system employing two orthogonally oriented plane polarizing filters: a polarizer and an analyzer, is known as a dark field plane polariscope. Any birefringence exhibited by the object placed between the crossed polarizing filters results in light passing through the polariscope. A similar device uses plane polarizing filters which are oriented with their planes of polarization parallel, and is referred to as a bright field linear polariscope. The presence of a birefringent object between the parallel polarizing filters results in some light not passing through the filters.
Loading of an object can create induced birefringence, which, when viewed through the plane polariscope, forms two sets of fringes. The first set of fringes, referred to as isoclinics, demarcate portions of the object where one of the principal stress directions is parallel to the axis of the polarizer. The second set of fringes, referred to as isochromatics, demarcate portions of the object where the difference of the principal stresses is zero or where the stress is of sufficient magnitude to retard the transmission of light by a whole number of wavelengths.
The isochromatic fringes may be viewed alone by eliminating the isoclinic fringes by passing the beam through a circular polariscope.
A circular polariscope consists of two polarizing filters and two one-quarter waveplates positioned between the polarizing filters. Again the polarizing filters may be arranged so that the planes of polarization are parallel, to produce a light field polariscope, or are perpendicular, to produce a dark field polariscope.
The isoclinic fringes are eliminated because the first one-quarter waveplate produces circularly polarized light in which the light no longer has a single axis of polarization, instead the axis of polarization rotates. The second one-quarter waveplate converts the beam back into linearly polarized light.
Photoelastic stress analysis suffers from a number of limitations which limit its usefulness. In order for the technique to be applied to a structure the structure must be constructed of a birefringent material or coated with a birefringent coating of a known thickness.
Constructing the structure of birefringence materials, which for practical reasons are typically low strength plastics, have inherent limitations when attempting to verify the structural response of high strength metals and composite structures. On the other hand, applying a coating to a structure has in the past required molding a layer of photoelastic plastic to the shape of the structure and then bonding the photoelastic layer to the structure. This technique is time consuming and requires considerable skill to avoid prestressing the plastic layer. Other techniques of coating the structure such as spraying or painting result in an uneven coating. Any nonuniformity in the coating thickness results in a proportional error in the measured stresses. Further spray on coating result in insufficient birefringence to apply classical photoelastic techniques with reasonable resolution.
Another problem with photoelastic stress analysis is that to determine stress at a particular point the number of fringes between a non stressed portion of the structure and the particular point must be counted. This makes the determination of the magnitude of the stresses in the structure subject to errors in counting the fringes or choosing a starting point for counting the fringes. The difficulty in accurately counting the number of fringe lines present can be overcome by choosing the thickness of the coating so the stresses produce less then a single fringe.
With this technique the changes in stress levels are represented by a brightness intensity within a single fringe band. However, known techniques for viewing the stress induced brightness level can not readily distinguish between minimum and maximum axes of stress.
What is needed is a photoelastic coating technique and a photoelastic analyzing technique and apparatus which produces full field determination of shear stress magnitude and direction.